"Luck out" means succeed by luck. For example,
I lucked out and found the last parking spot in the lot.
I wonder what phrase has opposite meaning and still uses "luck" as the verb? "luck in"?
I'm fairly certain that in colloquial English to have 'lucked out' has the opposite meaning as it would in America. So in England the same phrase will mean to have been unlucky. There's a brief reference to this in Bill Bryson's book 'Mother Tongue'. As an alternative for both sides of the Atlantic, to be 'out of luck' sort of works but it's not quite as pithy. Hope this helps.